Scenario Aggregation using Binary Decision Diagrams for Stochastic Programs with Endogenous Uncertainty

Modeling decision-dependent scenario probabilities in stochastic programs is difficult and typically leads to large and highly non-linear MINLPs that are very difficult to solve. In this paper, we develop a new approach to obtain a compact representation of the recourse function using a set of binary decision diagrams (BDDs) that encode a nested cover of the scenario set. The resulting BDDs can then be used to efficiently characterize the decision-dependent scenario probabilities by a set of linear inequalities, which essentially factorizes the probability distribution and thus allows to reformulate the entire problem as a small mixed-integer linear program. The approach is applicable to a large class of stochastic programs with multivariate binary scenario sets, such as stochastic network design, network reliability, or stochastic network interdiction problems. Computational results show that the BDD-based scenario representation reduces the problem size, and hence the computation time, significant compared to previous approaches.